Application of Linear Mean-Square Estimation in Ocean Engineering

The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method＇s overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations（adjacent to the concerning sea area） and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.

Numerical Solution of Mean-Square Approximation Problem of Real Nonnegative Function by the Modulus of Double Fourier Integral

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.

MEAN-SQUARE RADIUS OF GYRATION AND DIPOLE MOMENT OF POLY(METHYLPHENYLSILOXANE) CHAINS

The mean-square radius of gyration <S^2>,the mean-square dipole moment <D^2>,the mean-square end-to-end distance <R^2> and their temperature coefficients of unsymmetrical disubstituted poly(methylphenylsiloxane) (PMPS) chains, as a function of stereochemical structure,confomational energies and length of polymers,were studied by using an improved configurational-confomational statistical method based on the rotational-isomeric-state theory.It is found that the increase in isotacticity of P...

Mean-square composite-rotating consensus of second-order systems with communication noises

We study the mean-square composite-rotating consensus problem of second-order multi-agent systems with communication noises, where all agents rotate around a common center and the center of rotation spins around a fixed point simultaneously. Firstly, a time-varying consensus gain is introduced to attenuate to the effect of communication noises. Secondly, sufficient conditions are obtained for achieving the mean-square composite-rotating consensus. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithm.

Mean-square Almost Periodic Random Functions

In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.

A TSE based design for MMSE and QRD of MIMO systems based on ASIP

A Taylor series expansion(TSE) based design for minimum mean-square error(MMSE) and QR decomposition(QRD) of multi-input and multi-output(MIMO) systems is proposed based on application specific instruction set processor(ASIP), which uses TSE algorithm instead of resource-consuming reciprocal and reciprocal square root(RSR) operations.The aim is to give a high performance implementation for MMSE and QRD in one programmable platform simultaneously.Furthermore, instruction set architecture(ISA) and the allocation of data paths in single instruction multiple data-very long instruction word(SIMD-VLIW) architecture are provided, offering more data parallelism and instruction parallelism for different dimension matrices and operation types.Meanwhile, multiple level numerical precision can be achieved with flexible table size and expansion order in TSE ISA.The ASIP has been implemented to a 28 nm CMOS process and frequency reaches 800 MHz.Experimental results show that the proposed design provides perfect numerical precision within the fixed bit-width of the ASIP, higher matrix processing rate better than the requirements of 5G system and more rate-area efficiency comparable with ASIC implementations.

Lower bound on BER performance for maximal ratio combining with weighting errors

The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.

A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence

It is found that in free space, the curves of the mean-squared beam width may each have a cross point at a certain propagation distance Zc. For Gaussian array beams, the analytical expressions of zc are derived. For the coherent com- bination, Zc is larger than that for the incoherent combination. However, in non-Kolmogorov turbulence, the cross point disappears, and the Gaussian array beams will have the same directionality in terms of the angular spread. Furthermore, a short propagation distance is needed to reach the same directionality when the generalized exponent is equal to 3.108. In particular, it is shown that the condition obtained in previous studies is not necessary for laser beams to have the same directionality in turbulence, which is explained physically. On the other hand, the relative average intensity distributions at the position where the Gaussian array beams have the same mean-squared beam width are also examined.

Stochastic Iterative Learning Control With Faded Signals

Stochastic iterative learning control(ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists.Illustrative examples are provided to verify the effectiveness of the proposed schemes.

A novel SINR and mutual information based radar jamming technique

The improvements of anti-jamming performance of modem radar seeker are great threats to military targets. To protect the target from detection and estimation, the novel signal-to-interference-plus-noise ratio （SINR）-based and mutual information （Ml）-based jamming design techniques were proposed. To interfere with the target detection, the jamming was designed to minimize the S1NR of the radar seeker. To impair the estimation performance, the mutual information between the radar echo and the random target impulse response was used as the criterion. The spectral of optimal jamming under the two criteria were achieved with the power constraints. Simulation results show the effectiveness of the jamming techniques. SINR and MI of the SINR-based jamming, the MI-based jamming as well as the predefined jamming under the same power constraints were compared. Furthermore, the probability of detection and minimum mean-square error （MMSE） were also utilized to validate the jamming performance. Under the jamming power constraint of I W, the relative decrease of the probability of detection using S1NR-based optimal jamming is about 47%, and the relative increase of MMSE using Ml-based optimal jamming is about 8%. Besides, two useful jamming design principles are concluded which can be used in limited jamming power situations.

Unperturbed dimensions of atactic poly(dibenzyl itaconate)s

The unperturbed dimension and temperature character of poly(dibenzyl itaconate)s (PDBzI) are studied by a revised rotational isomeric state (RIS) method. The improved formulas of the mean-square radius of gyration, deduced by the pseudo-stereochemical equilibrium approach, may be used to investigate the configurational-conformational properties of atactic polymers with large side groups [poly(itaconates) for instance]. The calculated results showed that poly(itaconates) have larger dimension of the molecule than other vinyl polymers. Comparison of the dimension between considering and without considering side groups showed that the effect of large side groups on the unperturbed dimension for short-chain polymers is more obvious than that of long-chain polymers and, if the dimension of side groups increases, the effect also increases. The dimension differences of PDBzI between short-chain and long-chain polymers are investigated by the relation of characteristic ratios and temperature coefficients with temperature. Moreover, the dependence between the temperature coefficients and the tacticity of chains shows that the temperature characters of the isotactic, syndiotactic and atactic PDBzI chains have remarkable difference.

Global synchronization of general delayed complex networks with stochastic disturbances

In this paper, global synchronization of general delayed complex networks with stochastic disturbances, which is a zero-mean real scalar Wiener process, is investigated. The networks under consideration are continuous-time networks with time-varying delay. Based on the stochastic Lyapunov stability theory, Ito＇s differential rule and the linear matrix inequality （LMI） optimization technique, several delay-dependent synchronous criteria are established, which guarantee the asymptotical mean-square synchronization of drive networks and response networks with stochastic disturbances. The criteria are expressed in terms of LMI, which can be easily solved using the Matlab LMI Control Toolbox. Finally, two examples show the effectiveness and feasibility of the proposed synchronous conditions.

General Modified Split-Step Balanced Methods for Stiff Stochastic Differential Equations

A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations （ODEs） solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.

A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS

A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.

Novel delay-distribution-dependent stability analysis for continuous-time recurrent neural networks with stochastic delay

In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks （CRNNs） with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique （the reciprocally convex combination method）, less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. Two numerical examples show that our results are better than the existing ones.

Improved estimator of the continuous-time kernel estimator

There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases.

Moment Equations of Linear It Stochastic Systems with Applications

In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Ito stochastic systems are dervided. Based on the moment equations obtained, a necessary and sufficient condition for the mean-square asymptotic stability of linear Ito stochastic systems is obtained.For the time-invariant stochastic systems,the necessary and sufficient condition is just the same as the Hurwitz property of certain matrices related to the coefficient matrices of the systems. An algorithm STILSS is given for testing the mean-square asymptotic stability of time-invariant linear Ito stochastic systems.

Mean square stability of recurrent neural networks with random delay and Markovian switching

To establish easily proved conditions under which the random delayed recurrent neural network with Markovian switching is mean-square stability,the evolution of the delay was modeled by a continuous-time homogeneous Markov process with a finite number of states.By employing Lyapunov-Krasovskii functionals and conducting stochastic analysis,a linear matrix inequality (LMI) approach was developed to derive the criteria for mean-square stability,which can be readily checked by some standard numerical packages such as the Matlab LMI Toolbox.A numerical example was exploited to show the usefulness of the derived LMI-based stability conditions.

Asymptotical mean square stability of cellular neural networks with random delay

In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established results.

Discrete Sliding Mode Control of an Input-output System with Stochastic Disturbance

This paper presents the discrete adaptive sliding mode control of input-output non-minimum phase system in the presence of the stochastic disturbance. The non-minimum phase system can be transformed into a minimum phase system by a operator. According to the minimum phase system, the controller and the adaptive algorithm we designed ensures the stability of system and holds that the mean-square deviation from the sliding surface is minimized.